Generalized abundance conjecture

Let $X$ be a normal projective variety and let $\Delta$ be an effective $\mathbb{Q}$-divisor such that $(X,\Delta)$ is a klt pair. Write $\kappa(\cdot)$ for the Iitaka dimension and $\kappa_{\sigma}(\cdot)$ for the numerical dimension.

Generalized abundance conjecture.

$$\kappa(X,K_X+\Delta)=\kappa_{\sigma}(X,K_X+\Delta).$$

In particular, if $K_X+\Delta$ is nef, then it is semi-ample.

This is a central conjecture in the classification theory of algebraic varieties and would imply abundance for klt pairs with nef adjoint divisor. The source gives no resolution status.